In each program I have used from Corel Photo-Paint 11, Paint Shop Pro 5 and 7, to Gimp 2.6.11 the end result is exactly the same.

I select the background
Invert the selection to pull it out of the original
Paste the remaining image with transparent background
or make an alpha channel
The background needing to be transparent stays transparent.

The moment I save the image as a PNG, close the image, reopen it, check if the Mask/ Alpha channel data remains in tact, and it does, the transparency is completely removed and the background turns to white. This happens on every one of the programs and I am just at my wits end.

There must be something, an order of operations, a color scheme, a presetup step that -everyone- knows but me, that is preventing this from having a transparent background.

Can you post the image (before & after) or screen captures of the process (with the Layers list visible) ? How do you check "if the Mask/ Alpha channel data remains intact"? How do you "paste"? Edit/Paste (or Ctrl-V?)? "Edit/Paste as new layer"? If Ctrl-V, what do you do with the floating selection?